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Competing risks model time to first event and type of first event. An examplefrom hospital epidemiology is the incidence of hospital-acquired infection,which has to account for hospital discharge of non-infected patients as acompeting risk. An illness-death model would allow to further study hospitaloutcomes of infected patients. Such a model typically relies on a Markovassumption. However, it is conceivable that the future course of an infectedpatient does not only depend on the time since hospital admission and currentinfection status but also on the time since infection. We demonstrate how amodified competing risks model can be used for nonparametric estimation oftransition probabilities when the Markov assumption is violated.

A competing risks approach for nonparametric estimation of transition probabilities in a non-Markov illness-death model